det {base} | R Documentation

## Calculate the Determinant of a Matrix

### Description

`det` calculates the determinant of a matrix. `determinant` is a generic function that returns separately the modulus of the determinant, optionally on the logarithm scale, and the sign of the determinant.

### Usage

    det(x, ...)
    determinant(x, logarithm = TRUE, ...)

### Arguments

`x` | numeric matrix.
`logarithm` | logical; if `TRUE` (default) return the logarithm of the modulus of the determinant.
`...` | Optional arguments. At present none are used. Previous versions of `det` allowed an optional `method` argument. This argument will be ignored but will not produce an error.

### Value

For `det`, the determinant of `x`. For `determinant`, a list with components

`modulus` | a numeric value. The modulus (absolute value) of the determinant if `logarithm` is `FALSE`; otherwise the logarithm of the modulus.
`sign` | integer; either +1 or -1 according to whether the determinant is positive or negative.

### Note

Often, computing the determinant is not what you should be doing to solve a given problem.

Prior to version 1.8.0 the `det` function had a `method` argument to allow use of either a QR decomposition or an eigenvalue-eigenvector decomposition. The `determinant` function now uses an LU decomposition and the `det` function is simply a wrapper around a call to `determinant`.

### Examples

    (x <- matrix(1:4, ncol=2))
    unlist(determinant(x))
    det(x)

    det(print(cbind(1,1:3,c(2,0,1))))

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